I was responding particularly to your assertion that:
Winner-take-all majority rule voting is uniquely good at translating individual preference into social preference. If I had to pick a reason not to jettison the electoral college, this would be it.
It is completely relevant because Arrow’s criteria are basic measures of electoral fairness. Others have presented more properties that electoral rules should have, and fortunately there is enough of a vigorous debate on the subject that I was able to finagle a graduate degree in it.
It might be possible to make an argument that the chance of a split ballot is a more serious problem that failing to meet basic electoral criteria of fairness, but this is something that needs to be proven, not assumed.
Sure. The French election of 2002. The French ended up having to choose between a crook and a fascist due to strategic nomination. Chirac won by a landslide but at the same time, was loathed by almost eveyone who voted for him. Le Pen only got as far as he did because the left spammed the election with candidates.
This doesn’t really solve the problem at all. Even if a small party that meets the criteria of a super-proportional scheme can still have disproportionate influence in a coalition government. If a small party is pivotal, then its interests dominate the agenda.
Oh, sorry. This one is actually really simple. Basically, unrestricted domain means that the social choice function has to take into account absolutely all voter preferences to yield a complete and unique ranking of preferences.